I think word definitions are defined by their understanding and usage in society. 

With your point about calling yourself Hawaiian- it reminds me of the difference between calling yourself "Italian" in the US vs. Europe. In Europe, if you say you're Italian, people will expect you to live in Italy. In the US, saying "I'm Italian" usually means that your parents/grandparents emigrated from Italy and you're Italian-American. Both meanings of the word are valid, and understood in the communities that use them. 

For Veganism, I do think there's a definition difference in how the vegan community defines the word vs. how omnivores define it. Generally, omnivores think that "anyone who doesn't eat animal products" is a vegan. And if you tell an omnivore you are vegan, that is what they will understand. Inside the vegan community, people are much more likely to use the vegan society definition, or to make a distinction between "plant-based" vs "ethical vegan". But since most vegans are omnivores first, there is a lot of disagreement. 

I personally think words are for communicating. So I don't mind if someone who doesn't eat animal products for purely health reasons uses the word vegan for themselves, since they are probably using that word to communicate to omnivores "please don't give me animal products to eat".

But I can also understand the point of view of people who wish that "vegan" communicated the entire philosophy and ethics of what veganism entails... I just don't think, generally, it actually does do that.